Strength of Shafts.
Example 16.—A foundation bolt with square head (Fig. 368) is
secured by a cotter. Find D, b, and / in terms of d> where ft,fs, andyi
vary as I : | : 2 respectively. (Hons. Mach. Constr. Exam. 1886.)
Following the previous calculations :
D = ro8 d, b = 1-44 d^ and t—"*f>z d.
Torsional Stress-Action unallied with bending occurs
only in very short shafts. In any case the two actions Ihust be
separately considered. Fig. 369 shews a shaft under twist, the
external load being caused by the couple dxb c, while the in-
ternal resistance of the shaft is shewn by the couple exfg*
.-. External mometitjlmoment of resistance of section
where Zt, the modulus of section, is a number depending on the
size and shape of the section.
Strength of Solid Round Shaft.—Let r be the outer
radius of a solid shaft, Fig. 370. Imagining the section divided
into concentric rings:
Total stress on outer ring =/s X2irrxt (i)
Bntfs diminishes towards the centre because l>5 decreases:
.-. Total stress at any other ring ^ = -±fs x 21?^ x t (2)
* A couple is formed by a pair of equal and opposite forces, and can pro-
duce turning effect only, being represented by 'one force x "total arm.'